Title

Existence of a period-two solution in linearizable difference equations

Document Type

Article

Date of Original Version

12-1-2013

Abstract

Consider the difference equation x n + 1 = f (x n,⋯ xn -k), n = 0, 1, ⋯ where k ∈ { 1, 2⋯ } and the initial conditions are real numbers. We investigate the existence and nonexistence of the minimal period-two solution of this equation when it can be rewritten as the nonautonomous linear equation xn +l = ∑ i = 1 - l k g i x n + i , n = 0, 1, ⋯ where l, k ∈ { 1, 2⋯ } and the functions g i: R k + l → R. We give some necessary and sufficient conditions for the equation to have a minimal period-two solution when l = 1. © 2013 E. J. Janowski and M. R. S. Kulenović.

Publication Title

Discrete Dynamics in Nature and Society

Volume

2013

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